For Numbers 5 and 6: Let X₁, X2 be jointly normally distributed with zero means, unit variances, and correlation coefficient, p. Let S be a x²(n) random variable that is independent of (X₁, X2). Then the joint 1 Y ₂ = X² / √5/n distribution of Y₁ =X₁/√√S/n and Y₂ is known as central bivariate t-distribution. 5. Find the joint probability density function of (X₁,Y₂). 6. Find the marginal probability density functions of Y₁ and Y2, respectively.
For Numbers 5 and 6: Let X₁, X2 be jointly normally distributed with zero means, unit variances, and correlation coefficient, p. Let S be a x²(n) random variable that is independent of (X₁, X2). Then the joint 1 Y ₂ = X² / √5/n distribution of Y₁ =X₁/√√S/n and Y₂ is known as central bivariate t-distribution. 5. Find the joint probability density function of (X₁,Y₂). 6. Find the marginal probability density functions of Y₁ and Y2, respectively.
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Transcribed Image Text:For Numbers 5 and 6: Let X₁, X2 be jointly normally distributed with zero means, unit variances, and
correlation coefficient, p. Let S be a x²(n) random variable that is independent of (X₁, X2). Then the joint
1 Y ₂ = X² / √5/n
distribution of Y₁ =X₁/√√S/n
and Y₂
is known as central bivariate t-distribution.
5. Find the joint probability density function of (X₁,Y₂).
6. Find the marginal probability density functions of Y₁ and Y2, respectively.
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